A set of free boundary results from the VMEC equilibrium code [1]} is calculated for the vacuum CFQS configuration (\(\beta _{th}=0\) ) and finite thermal \(\beta \)  cases with \(\beta _{th}=0.01\) , \(0.02\)  and \(0.03\) . The effect of the bootstrap current is included in the equilibria, calculated using the code BOOTSJ [2]}. The magnetic field at the magnetic axis is 1 T, the toroidal field period number is 2, the averaged inverse aspect ratio is \(\varepsilon =0.25\)  and the major radius \(R_{0} = 1\)  m. The energy of the injected particles by the NBI is \(T_{f}(0) = 30\)  keV and the nominal energy of the EP resulting in an averaged Maxwellian energy equal to the average energy of a slowing-down distribution is 17 keV. Figure REF  shows the main profiles of the thermal plasma. The thermal \(\beta \)  of the model increases because the thermal plasma density increases. Figure REF  shows the EP density profiles used in the study. The energy of the EP is assumed constant, with no radial dependency, for simplicity. It should be noted that the EP density profile and energy is the same in the simulations for the vacuum configuration and finite \(\beta _{th}\) . The EP \(\beta \)  (\(\beta _{f}\) ) is defined at the magnetic axis. The growth rate (\(\gamma \tau _{A0}\) ) is normalized to the Alfvén time at the magnetic axis (\(\tau _{A0} = R_0 (\mu _0 \rho _m)^{1/2} / B_0\) ).
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